An infinite number of
filter transfer functions exist. A handful are commonly
used as a starting point due to certain characteristics.
The table following the plots lists properties of the
filter types shown below. Not given  due to complex
numerical methods required  are the Cauer
(Elliptical) filters that exhibit equiripple
characteristic in both the passband and the stopband.
Phase information may
be gleaned from the transfer functions by separating
them in to real and imaginary parts and then using
the relationship:
Phase: q
= tan^{1} (Im / Re)
Group delay is defined
as the negative of the first derivative of the phase
with respect to frequency, or
Group Delay:
